Given two algebras $A$, $B$ in terms of generators and relations, is there some software/algorithm which can check whether $A \cong B$? It looks like this is not true in general, so is there software that can check this in special cases?
2026-02-22 21:06:05.1771794365
Which software can check whether two algebras are isomorphic?
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No, this problem is undecidable. If it were decidable then you could determine whether a finitely presented group $G$ is trivial, by checking whether its group algebra $k[G]$ is isomorphic to $k$ (over $k$); this is known to be undecidable.
The corresponding question for commutative algebras is not known to be decidable or undecidable, at least as of 2012.